What Boehner is calling on Pelosi to do is have each member of congress stand up and announce their vote. It is not clear if Boehner thinks that Pelosi will actually comply or just wants more fodder for ads and talking points. I would think Pelosi would not want to do this to try and protect the Democrats in swing districts who know their constituents do not want them voting for this bill.
"Dear Speaker Pelosi:
It appears the House of Representatives will proceed with plans to vote this weekend on President Obama’s health care legislation, despite the well-documented objections of the American people to both the contents of the bill and the manner in which the Democratic leadership hopes to pass it.
This weekend’s votes will be among the most consequential votes we will ever cast as Members of Congress. As such, it is my belief that every Member should stand before the American people and announce his or her vote as the final decision is made.
With this in mind, I request that you use your discretion under the Rules of the House of Representatives, Clause 2 and 3 of House Rule XX, to conduct the record vote by call of the roll for both adoption of the Senate health care bill (i.e. the Senate Amendment to H.R. 3590, as passed on Christmas Eve this past year) and for the rule making that bill in order.
Thank you for your consideration of this request."